The sum of two numbers is $58$, and their difference is $30$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 58}$ ${x-y = 30}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 88 $ $ x = \dfrac{88}{2} $ ${x = 44}$ Now that you know ${x = 44}$ , plug it back into $ {x+y = 58}$ to find $y$ ${(44)}{ + y = 58}$ ${y = 14}$ You can also plug ${x = 44}$ into $ {x-y = 30}$ and get the same answer for $y$ ${(44)}{ - y = 30}$ ${y = 14}$ Therefore, the larger number is $44$, and the smaller number is $14$.